Although DBI inflation models were greatly successful, it was realized
that the microscopic bound on the maximal field variation due to
compactification is able to put strong constraints on the throat
volume [1]} and bulk volume [2]}. These
issues, together with the Lyth bound, lead to a model independent
upper bound on the tensor-to-scalar ratio which turns out to be
inconsistent with the stringent observational upper bounds on
gravitational waves that are produced by the inflationary
dynamics [3]}. Moreover, a viable reheating process,
which typically involves brane-antibrane
annihilation [4]}, is highly constrained due to
overproduction of long-lived Kaluza-Klein (KK)
modes [5]}.
